A controller including a detecting member detecting a machining position where a pivoting axis is reversed in machining by the machine tool based on the control data, an allowable position error setting member setting an allowable position error between a commanded machining position and an actual machining position, an allowable acceleration deciding member deciding the allowable acceleration about the pivoting axis based on a distance from the machining position of the reversed axis to a center of the pivoting axis and based on the allowable position error being set, and a controlling member controlling a velocity about the driving axis based on the allowable acceleration.